The generator matrix

 1  0  0  1  1  1  0 X^2+2 X^2+2 X^2+2  1  1  1  1 X^2+X  1  1 X+2  1  X  1 X^2+X X^2+X+2  1  1 X+2  1  1 X^2+X+2  1  1 X^2  0  1 X^2  1  1  X X+2  1  1 X^2+X  1  1 X^2+2  1  1  1  1  1 X^2  1 X+2 X^2+X+2  1  0  1 X^2+X+2 X^2+X  1  1  1  1  2  1  0  1  1 X^2+2  1  1  X  1  1  X  X  1
 0  1  0  0 X^2+1 X^2+3  1  X  1  1 X^2+2 X^2 X^2+1 X^2+1 X^2 X^2+X+1 X^2+X  1 X+2  1 X+3  1 X^2+X+2 X+2 X^2+X+2  1 X^2+X+1 X^2+X+3 X+2 X^2 X+3  1  1  1  1 X^2+3 X+2 X^2+2  1 X+2 X^2+3  1 X^2+X X^2+2  1  3 X+3  X X^2+3 X^2  X  1  1  1 X^2+X+3  1  2 X^2+X  1 X+1 X^2+X+3  0  0 X^2+X+2  3  1  3  2  1 X^2+2 X^2+X+3  1  2 X^2+X+3  2  X  0
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1  X  3  X X^2+3  3 X^2+X+2  1 X^2+X  X X^2+2 X+3 X^2+1  1 X^2+X+3  1  1  0 X^2+X+2 X+1 X^2  1 X+2  2  X X^2+X+3 X^2+1 X^2+2 X^2+X+3  0  1  2 X+3 X^2+X+3 X+3  X X^2+3 X^2+X+3 X^2+2 X^2+3 X^2+3 X+2 X^2+X+3  1  0  X X^2+1 X^2+X+3 X^2+1  0  1 X^2+X+1 X+1  X X^2+2 X^2+1  1  3 X+3  1 X+1 X^2+X+2 X^2+2 X^2+X+3 X^2+2 X^2+X X+2  1  1  0
 0  0  0 X^2 X^2  0 X^2 X^2+2 X^2  2 X^2  0  2 X^2+2 X^2 X^2 X^2+2  0  2 X^2  0  2  0 X^2+2  2 X^2 X^2+2 X^2 X^2 X^2+2  2  0  2 X^2+2 X^2  2 X^2  2 X^2+2 X^2+2 X^2+2 X^2  2 X^2+2 X^2+2 X^2+2 X^2  0  0  0  0  2  2  0  2 X^2+2 X^2+2 X^2+2  0  0 X^2+2  2  0  2 X^2  0  0  2  2  0 X^2 X^2  0  2 X^2+2  0  0

generates a code of length 77 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+114x^71+664x^72+1300x^73+1628x^74+2026x^75+2093x^76+1908x^77+1785x^78+1478x^79+1163x^80+796x^81+544x^82+434x^83+250x^84+98x^85+47x^86+28x^87+12x^88+8x^89+2x^90+1x^92+2x^93+2x^94

The gray image is a code over GF(2) with n=616, k=14 and d=284.
This code was found by Heurico 1.16 in 3.42 seconds.